{
  "id": "0906.5375",
  "version": "v3",
  "published": "2009-06-29T21:33:48.000Z",
  "updated": "2009-11-30T10:33:29.000Z",
  "title": "Quasi-Invariant measures, escape rates and the effect of the hole",
  "authors": [
    "Wael Bahsoun",
    "Christopher Bose"
  ],
  "comment": "15 pages",
  "categories": [
    "math.DS"
  ],
  "abstract": "Let $T$ be a piecewise expanding interval map and $T_H$ be an abstract perturbation of $T$ into an interval map with a hole. Given a number $\\ell$, $0<\\ell<1$, we compute an upper-bound on the size of a hole needed for the existence of an absolutely continuous conditionally invariant measure (accim) with escape rate not greater than $-\\ln(1-\\ell)$. The two main ingredients of our approach are Ulam's method and an abstract perturbation result of Keller and Liverani.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2009-11-30T10:33:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37A05",
      "37E05"
    ],
    "keywords": [
      "escape rate",
      "quasi-invariant measures",
      "abstract perturbation result",
      "piecewise expanding interval map",
      "ulams method"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0906.5375B"
    }
  }
}